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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.08124 |
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| _version_ | 1866909424536256512 |
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| author | Wang, Xi Wang, Xiaoyi Solo, Victor |
| author_facet | Wang, Xi Wang, Xiaoyi Solo, Victor |
| contents | In this paper, we develop a novel method for deriving a global optimal control strategy for stochastic attitude kinematics on the special orthogonal group SO(3). We first introduce a stochastic Lie-Hamilton-Jacobi-Bellman (SL-HJB) equation on SO(3), which theoretically provides an optimality condition for the global optimal control strategy of the stochastic attitude kinematics. Then we propose a novel numerical method, the Successive Wigner-Galerkin Approximation (SWGA) method, to solve the SL-HJB equation on SO(3). The SWGA method leverages the Wigner-D functions to represent the Galerkin solution of the SL-HJB equation in a policy iteration framework, providing a computationally efficient approach to derive a global optimal control strategy for systems on SO(3). We demonstrate the effectiveness of the SWGA method through numerical simulation on stochastic attitude stabilization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Kinematic Optimal Control on SO(3) Wang, Xi Wang, Xiaoyi Solo, Victor Optimization and Control In this paper, we develop a novel method for deriving a global optimal control strategy for stochastic attitude kinematics on the special orthogonal group SO(3). We first introduce a stochastic Lie-Hamilton-Jacobi-Bellman (SL-HJB) equation on SO(3), which theoretically provides an optimality condition for the global optimal control strategy of the stochastic attitude kinematics. Then we propose a novel numerical method, the Successive Wigner-Galerkin Approximation (SWGA) method, to solve the SL-HJB equation on SO(3). The SWGA method leverages the Wigner-D functions to represent the Galerkin solution of the SL-HJB equation in a policy iteration framework, providing a computationally efficient approach to derive a global optimal control strategy for systems on SO(3). We demonstrate the effectiveness of the SWGA method through numerical simulation on stochastic attitude stabilization. |
| title | Stochastic Kinematic Optimal Control on SO(3) |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.08124 |